Treating the estimates \(\hat{\psi }_i\)  as given numbers, the method of EBLUP leads to the predictions of domain proportions (REF ) that are expressed as the linear combinations [1]}
\(\hat{\theta }_i^{\mathrm {FH}}=\hat{\theta }_i^{\mathrm {FH}}(\hat{\psi }_i)=\hat{\gamma }_i\hat{\theta }_i^{\mathrm {d}}+(1-\hat{\gamma }_i)\mathbf {z}_i^{\prime } \hat{}, \quad \text{with} \quad \hat{\gamma }_i=\frac{\hat{\sigma }_v^2}{\hat{\psi }_i+\hat{\sigma }_v^2}, \qquad i=1,\ldots , M,\) 
